The diagram of the pentagon is missing, so i have attached it.
Answer:
|AE| = 130 m
|DE| = 150 m
Perimeter of pentagon = 720 m
Step-by-step explanation:
From the diagram, we can find AE from pythagoras theorem;
|AE| = √(|AA'|² + 50²)
Where AA' is the length from A to the perpendicular angle.
Now, AB = 150, and A'B is parallel to 30 m. Thus, A'B = 30
AA' = AB - A'B = 150 - 30
AA' = 120
Thus;
|AE| = √(120² + 50²)
|AE| = √(14400 + 2500)
|AE| = √16900
|AE| = 130
Similarly,
|DE| = √(|DD'|² + |ED'|²)
ED' = BC - 50
ED' = 140 - 50
ED' = 90
Also, DD' is parallel to AA' and is = 120
Thus;
|DE| = √(120² + 90²)
|DE| = √22500
|DE| = 150
Perimeter of pentagon = 150 + 130 + 150 + 150 + 140 = 720
The expected value of the game is its average earnings
- The expected value of a round is $2.23
- The expected value when the game is played 755 times is $1683.65
<h3>How to determine the expected value of a round</h3>
There are 12 cards with a value of 4 or less.
So, the probability of selecting a card with a value of 4 or less is:

The probability of selecting a card with a value more than 4 is the complement of the above probability.
So, we have:


The expected value is then calculated as:

Evaluate


Simplify

Hence, the expected value of a round is $2.23
<h3>The expected value when the game is played 755 times</h3>
In (a), we have:

In probability, we have:

So, we have:


Hence, the expected value when the game is played 755 times is $1683.65
Read more about expected values at:
brainly.com/question/15858152
<u>Answer:</u>
The correct answer option is b)
.
<u>Step-by-step explanation:</u>
We are given that the first urn contains 7 white balls and 7 yellow balls and the second urn contains 3 white balls and 6 yellow balls. We are to find the probability that both balls drawn are white.
This means that the first must be white and the second ball must also be white.
P (w, w) =
×
= 
Therefore, the probability that both the balls drawn are white is 1/6.
cos (arctan (1))=
arctan (1) = 45 take it to the third quadrant = add 180 = 225
cos (225) = -1 / sqrt(2)
never leave a sqrt in the denominator
= -1 /sqrt(2) * sqrt(2)/sqrt(2)
= -sqrt(2)/2
sin (arccos (1/2)
arccos (1/2) = 60 take it to the 4th quadrant -60 degrees
sin (-60)
- sin 60
- sqrt(3)/2